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John and Mary were each paid x dollars in advance to do a certain job together

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John and Mary were each paid x dollars in advance to do a certain job together, John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance ? 

(A) 4y
(B) 5y 
(C) 6y 
(D) 8y 
(E) 9y

Official Answer

1 Answer

Suppose the hourly rate of wages is $1.
Since John works for 10 hours he earns $1*10 = $10 (=J)
And As Mary works 8 hours (10 - 2), she earns = $8 (=M)
So total advance payment = J+M = $18
Each of them receives x dollars in advance, a = 18/2 => $9 each
John has been given the advance payment of $9, but he must earn $10
Similarly Mary has been give the advance payment of $9 but she must $8
Thus the difference is $1. Mary should give John $1.
The question asks for the amount that John is paid in advance: $9.
This is our target.
Now we plug y=1 into the answers to see which yields our target of 9.
Only answer choice E works:
9y = 9*1 = 9.
The correct answer is E.
answered Sep 27, 2014 by Partner (696 points)
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